Best Known (15, ∞, s)-Nets in Base 27
(15, ∞, 96)-Net over F27 — Constructive and digital
Digital (15, m, 96)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (15, 95)-sequence over F27, using
- t-expansion [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- t-expansion [i] based on digital (11, 95)-sequence over F27, using
(15, ∞, 136)-Net over F27 — Digital
Digital (15, m, 136)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (15, 135)-sequence over F27, using
- t-expansion [i] based on digital (13, 135)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
- t-expansion [i] based on digital (13, 135)-sequence over F27, using
(15, ∞, 443)-Net in Base 27 — Upper bound on s
There is no (15, m, 444)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (15, 885, 444)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(27885, 444, S27, 2, 870), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 462 824456 258047 903210 779447 993592 086183 688118 293745 825760 836455 414974 217969 750945 860060 858873 830216 482040 394501 275752 341588 610118 750368 525063 064679 567218 863672 796041 514278 316155 900927 249921 045139 516578 809751 503781 831144 211054 539446 203209 963061 468082 658956 597714 056200 658273 813308 024393 262053 681065 454426 106040 832291 542177 717522 276175 679080 988229 065023 775818 894315 952298 885743 272853 894115 287386 214609 833201 471546 787326 386004 643979 773204 212862 274295 740862 112915 170390 407868 985013 519491 000103 626276 394598 901927 157128 351986 184554 228087 484535 983697 786961 198846 091848 065325 533113 406597 509597 305880 157688 475638 018611 371615 366621 585560 855780 600778 797587 693820 577842 504268 066693 291864 093677 894884 287196 418354 482848 224807 827890 503527 297474 933951 276643 328804 636856 317728 309231 728074 563460 082773 963537 157503 997089 794310 399154 203024 998776 848474 226680 989613 451556 825241 703871 086487 685792 770912 277296 187046 036133 224959 029637 826411 128200 259339 451393 402875 258060 822279 682936 347768 637265 706874 162897 570373 638078 301081 051622 519444 537933 407232 335611 484463 215026 220165 035974 148364 641839 615679 486287 395725 688806 297237 356473 749301 280959 568238 370200 820894 474293 689538 689135 777175 889455 301377 624556 220693 308190 980410 413877 893673 719404 850937 956186 641788 084729 357117 525212 366651 005427 732060 135067 / 67 > 27885 [i]
- extracting embedded OOA [i] would yield OOA(27885, 444, S27, 2, 870), but